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1 ECE 30L, Exam Fall 05 Equatio Sht Plas tar off this ag ad k it with you Gral Smicoductor: 0 i ( EF EFi ) kt 0 i ( EFi EF ) kt Eg i N C NV kt 0 0 V IR L, D, τ, d d τ c g L D kt I J diff D D µ * m σ (µ + µ ) J dx dx A m V C ρ µ J drift σ E Juctios: kt! N a N d Vbi l i c DS ox! ε ε Na s 0 x V bi N d ( N a + N d )! ε ε Nd x s 0 Vbi N a ( N a + N d ) V! V a a! ε sε 0 N a + N d! ε sε 0 N a + N d kt kt x x W Vbi WRB Vbi + VR ) ( ) 0 ( ) 0 ( Na Nd Na Nd! (! Va + xl x (! Va +! x +x! kt L δ (x) 0 * kt - EF EFi + kt l EF EFi kt l δ (x) 0 * - *) -, *) -, i i! V!! Va Wi kta kt D D I 0 0 J J ID J S J S + gd DQ Cd ( I 0τ 0 + I 0τ 0 ) rc τ V L L r V 0 t d t MOS Caacitors: C ( acc ) Cox tox C ( dl )!ε tox + ox xd εs C mi!ε tox + ox xdt εs C FB VFB φ ms Qss φ s EFi Cox - ty: φms! ε ε φ E! φ χ + g + φ f φ f Vt l N a xd s 0 s N a i - ty: φms! ε ε φ E! φ m χ + g φ f φ f Vt l N d xd s 0 s N d i bulk EFi surf VTN QSD ( max) Cox! εε! ε ox s 0 tox + Vt εs N a,d + VFB + φ f VTP m QSD ( max) Cox! 4ε sε 0φ f xdt N a xdt! 4ε ε φ s 0 f N d + VFB φ f QSD ( max) N a xdt QSD ( max) N d xdt MOSFETs: gm! δ ( log ( I D )) δid gm gm SS δv ft π (C + C ) π C δvgs gst M G GS CM CgdT (+ gm RL ) W µ Cox W µ Cox Wµ C ID (VSG + VT ) VSD VSD I D ( sat ) (VSG + VT ) K ox k µ Cox - ty: L L L W µ Cox W µ Cox W µ Cox k µ Cox - ty: I D L (VGS VT ) VDS VDS I D ( sat ) L (VGS VT ) K L h π q.60x0 9 C Si at T 300 K: i.5x00 cm- 3, Eg. V, εs.7 SiO: εox 3.9 k 8.6x0 5 V / K.38x0 3 J / K h 4.4x0 5 V s 6.63x0 34 J s! kt 0.06 V at room tmratur

2 Exam Smicoductor Dvics ECE 30L, Exam Fall 05 Nam: Nt ID: 5 qustios. 0 oits r qustio. Partial crdit will b giv wh ossibl (MUST show work). Plas writ atly (lgibly). Wh giv, writ fial aswrs i th rovidd boxs. Show your work (NEATLY) whvr it is ossibl (us th back of ags if dd)! Good luck!

3 ECE 30L, Exam Fall 05 ) Juctio Diods Cosidr a silico juctio diod with ara of 0-4 cm at T 300K ad th followig aramtrs: - sid: N a 0 4 cm sid: N d 0 7 cm - 3 τ 0-7 s τ 0-6 s µ 00 cm /V- s µ 800 cm /V- s µ 400 cm /V- s µ 300 cm /V- s a. Sktch th thrmal quilibrium rgy bad diagram for this diod i th sac rovidd. B sur to iclud a accurat valu (ad rasoably accurat sktch) for E F E Fi o both sids of th juctio ad of V bi. B sur to labl E c, E v, E F, ad E Fi. Tak ach box to b 0.5 V o all sids b. Now sktch th rgy bad diagram udr a alid forward bias, V a 0.5 V. B sur to idicat V a i som fashio o your diagram ad sktch i th quasi- Frmi lvls. c. Calculat th amout of currt (I ) flowig through th diod if V a 0.5 V. I d. Comlt th qualitativ sktch (giv o th right) of th currt dsity i th diod, icludig th curvs for J total, J ad J o ach sid of th juctio ad labl J (- x ) ad J (x ). J. If this diod wr itgratd ito th circuit giv blow ad V a 0.5 V was th voltag drod across th diod, what would th voltag dro ad currt flow b for th rsistor? V a + ( x x x 3V kω VR IR

4 ECE 30L, Exam Fall 05 ) MOS Caacitors Giv th rgy bad diagram of a MOS caacitor o th right, with th aramtrs idicatd blow, aswr th qustios. V FB 0.06 V, Q ss 0, t ox 7 m, f 0 Hz, ϕ f V a. I th sac rovidd blow th bad diagram, sktch th bad diagram for wh th MOS caacitor is at V G 0 V, lablig E Fs, E Fi, E C, E V, ad ϕ s. E Fm 0.V E Fi E Fs 0.3V b. O th giv bad diagram, sktch i th alid gat voltag, V G. c. What is th alid gat voltag, V G? d. What is th doig ty ad dsity?. What is th surfac ottial? a. f. Calculat th thrshold voltag, V T. Is this MOS caacitor oratig i strog ivrsio? g. Sktch th C- V curv for this caacitor o th axs blow ad labl th oit at which th caacitor is oratig alog with V T, V FB, C ox, ad C mi. E Fm *Show your work (atly) whvr ossibl (us back of ag if dd)! g. C V G d. ty c.. VG N ϕs f. VT Strog Ivrsio?

5 3) MOS Caacitor CONCEPTUAL Aswr th qustios i th sacs rovidd: ECE 30L, Exam Fall 05 For th MOS caacitor bad diagram o th lft: a. Is th caacitor i thrmal quilibrium? b. Is th smicoductor i thrmal quilibrium? c. What ty of smicoductor is this? d. Dos ϕ ms 0 for this caacitor?. What olarity V G (ositiv or gativ) is dd to orat th caacitor i dltio mod? f. Sktch oto th bad diagram what would ha if V G ϕ f wr alid, showig all rlvat chags that would tak lac. g. What mod would th caacitor b oratig i with this alid voltag (from art f)? For th MOS caacitor C- V curv o th lft: h. Is th caacitor oratig at low or high f? i. What ty of smicoductor is this? j. Idicat o th curv whr th dltio mod of oratio is takig lac. k. Rdraw th C- V curv for th cas of havig som gativ fixd chargs addd to th oxid. l. Brifly dscrib what would ha to th C- V curv if itrfac tras wr rst? E Fm C M O S z E Fs E Fi V G For th MOS caacitor block charg diagram: m. What ty of smicoductor is this?. What mod is this caacitor oratig i? o. O th diagram, sktch i what would ha as a small ac sigal is alid to th caacitor.. O th diagram, sktch i what it would look lik to hav som ositiv fixd charg rst i th oxid. q. From this diagram, ca you tll whthr or ot V FB 0 V?

6 ECE 30L, Exam Fall 05 4) MOSFETs Cosidr a Si MOSFET with th charactristics show blow. Labl th ty of charactristics that ach lot shows o th lis blow th lots. S S charactristics charactristics Th voltag, V GS is coctd with th ositiv trmial to th gat of th MOSFET ad th voltag, V DS has th ositiv trmial to th drai. Th dvic has V DD V with V T V, t ox m, W µm, k k 0.50 ma/v, ad a load rsistac of 5 Ω. Aswr th qustios or xtract th aramtrs blow ad, wh ossibl, show how ach was xtractd o th lots. a) Subthrshold swig b) Trascoductac c) O- currt d) Is th MOSFET - ty or - ty? ) Mobility f) W/L g) If th gat ovrlas th drai by 0.*L, what will th cut- off frqucy b? ft

7 ECE 30L, Exam Fall 05 5) MOSFETs CONCEPTUAL Aswr th qustios i th sacs rovidd: For th MOSFET schmatic o th lft: a. If this is a - ty MOSFET, labl th sourc, drai, ad substrat rgios with th aroriat doig. b. Sktch i th dltio rgio ad ivrsio layr for th coditio wh th MOSFET is oratig i th liar rgio. c. Will thr b ovrla caacitac i this MOSFET? d. Which will b gratr, C gs or C gd?. O th schmatic, idtify th dimsio L. f. I th bad diagram startd to th right, sktch th MOS caacitor ortio of this MOSFET udr th abov coditios, lablig E Fs, E Fi, E C, E V, V SG, ad ϕ s. E Fm I D k V DD V SD DS For th curvs i th lot to th lft: g. Ca th thrshold voltag b dtrmid from this lot? h. What ty of MOSFET is this? i. Sktch th V DS (sat) li o th lot. j. If th d curv from th to is from V GS V DD, idicat th o- currt o th lot. k. I th mty schmatic giv blow, sktch th MOSFET from this lot oratig at th idicatd oit labld k. O your sktch, labl th sourc, drai, ad substrat rgios with aroriat doig ad iclud th dltio rgio ad ivrsio layr. If alicabl, labl L, ΔL, ad iclud th caacitacs C gd, C gd, C gs, ad C gs.